Write the number in standard form a 2) \( \frac{-5+\sqrt{-75}}{10} \)

To express the number \( \frac{-5+\sqrt{-75}}{10} \) in standard form, which is \( a + bi \) for complex numbers, follow these steps: 1. **Simplify the Square Root:** \[ \sqrt{-75} = \sqrt{-1 \times 75} = \sqrt{-1} \times \sqrt{75} = i \times \sqrt{75} \] 2. **Simplify \( \sqrt{75} \):** \[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3} \] So, \[ \sqrt{-75} = 5i\sqrt{3} \] 3. **Substitute Back into the Original Expression:** \[ \frac{-5 + \sqrt{-75}}{10} = \frac{-5 + 5i\sqrt{3}}{10} \] 4. **Separate the Real and Imaginary Parts:** \[ = \frac{-5}{10} + \frac{5i\sqrt{3}}{10} \] 5. **Simplify the Fractions:** \[ = -\frac{1}{2} + \frac{\sqrt{3}}{2}i \] 6. **Write in Standard Form:** \[ \boxed{-\frac{1}{2} + \frac{\sqrt{3}}{2}i} \] **Final Answer:** \[ -\frac{1}{2} + \frac{\sqrt{3}}{2}\,i \]